Exact Solution of an Exclusion Model in the Presence of a moving Impurity

Abstract

We study a recently introduced model which consists of positive and negative particles on a ring. The positive (negative) particles hop clockwise (counter-clockwise) with rate 1 and oppositely charged particles may swap their positions with asymmetric rates q and 1. In this paper we assume that a finite density of positively charged particles $\rho$ and only one negative particle (which plays the role of an impurity) exist on the ring. It turns out that the canonical partition function of this model can be calculated exactly using Matrix Product Ansatz (MPA) formalism. In the limit of infinite system size and infinite number of positive particles, we can also derive exact expressions for the speed of the positive and negative particles which show a second order phase transition at $q_c=2\rho$. The density profile of the positive particles on the ring has a shock structure for $q\le q_c$ and an exponential behaviour with correlation length $\xi$ for $q\ge q_c$. It will be shown that the mean-field results become exact at q=3 and no phase transition occurs for q>2.

9 pages,4 EPS figures. To be appear in JPA

References in corpus (3)

• Spatial Particle Condensation for an Exclusion Process on a Ring
• Spontaneous Breaking of Translational Invariance and Spatial Condensation in Stationary States on a Ring: I. The Neutral System
• Yang-Lee Theory for a Nonequilibrium Phase Transition

Cited by in corpus (9)

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• Critical phenomena and universal dynamics in one-dimensional driven diffusive systems with two species of particles
• Matrix Product States of Three Families of One-Dimensional Interacting Particle Systems
• Numerical Study of Phase Transition in an Exclusion Model with Parallel Dynamics
• Exact Solution of a Reaction-Diffusion Model with Particle Number Conservation
• Multi species asymmetric simple exclusion process with impurity activated flips
• Shock in a Branching-Coalescing Model with Reflecting Boundaries
• Phase Separation Transition in a Nonconserved Two Species Model
• Travelling with/against the flow. Deterministic diffusive driven systems